Professor Poirier | D710 | Fall 2024
6(a). True – The transpose of an invertible matrix is an invertible matrix
Ex:
A=
det(A) = -2*-1/2 – 3/2 = -1/2
A^T=
det(A^T) = -2*-1/2 – 3/2 = -1/2
6(b). False – Every system of linear equations has exactly one solution
Infinite Solutions:
x+y=1, 2x+2y=2
2x+2y=2 is basically x+y=1 when divided by 2.
Graph:
No Solutions:
x+y=0, x+y=1
One Solutions:
x+2y=1, 2x+2y=2
Intersects at (1,0)
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